Problem: Solve for $x$ and $y$ using elimination. ${2x-6y = -10}$ ${x-5y = -13}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${2x-6y = -10}$ $-2x+10y = 26$ Add the top and bottom equations together. $4y = 16$ $\dfrac{4y}{{4}} = \dfrac{16}{{4}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x-6y = -10}\thinspace$ to find $x$ ${2x - 6}{(4)}{= -10}$ $2x-24 = -10$ $2x-24{+24} = -10{+24}$ $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ You can also plug ${y = 4}$ into $\thinspace {x-5y = -13}\thinspace$ and get the same answer for $x$ : ${x - 5}{(4)}{= -13}$ ${x = 7}$